To generate equivalent expressions with only positive exponents, we can use the properties of exponents.
First, we know that any number raised to the power of 0 is equal to 1. Therefore, 4^0 is equal to 1.
Next, to convert 5^(-2) to a positive exponent, we can use the property that a^(-n) is equal to 1/a^n. So, 5^(-2) is equal to 1/5^2, which is equal to 1/25.
Similarly, to convert (-2)^(-3) to a positive exponent, we can rewrite it as 1/(-2)^3 using the same property. (-2)^3 is equal to -8, so (-2)^(-3) is equal to 1/(-8), which simplifies to -1/8.
Now we can substitute these values back into our expression:
4^0 * 5^(-2) / (-2)^(-3) = 1 * 1/25 / (-1/8)
When dividing by a fraction, it is equivalent to multiplying by its reciprocal. So, we can rewrite the expression as:
1 * 1/25 * (-8/-1)
Multiplying the numerators and denominators:
= 1 * (-8) / (25 * -1)
= -8 / -25
Finally, simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1:
= 8 / 25
Therefore, the simplified fraction equivalent to 40 * 5^(-2) / (-2)^(-3) is 8/25.
Question%0D%0AApply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)%0D%0A40 ⋅ 5^−2/(−2)^−3=
1 answer